1) партию в шахматы translates as "a game of chess" I think? Wondering if this is some special use of в I am unaware of. I thought "a game of chess" would be партию шахмат using the genitive so I am unclear on that.

2) до того is "until that time" or "until that point" or something like that I think? I have looked up both words and their uses and still am not sure how it is being used here exactly.

3) I know как has a lot of different uses. Here I'm not sure what it is. Is it "as Andre came in"? Honestly, this whole cluster "до того, как пришёл Андрей" has me confused.

This is my best translation at this point.

When we arrived in class, the teacher had already gone home. We had plenty of time to play a game of chess before Andre arrived.

Sorry there are so many points to cover. If it wasn't for this forum I don't know how I would go about learning this language. Any help is appreciated. Thank you.

1) партию в шахматы translates as "a game of chess" I think? Wondering if this is some special use of в I am unaware of. I thought "a game of chess" would be партию шахмат using the genitive so I am unclear on that.

The preposition в (+accusative) is used with the verb играть ‘to play’ before the name of the game:игра́ть в ша́хматы ‘play chess’игра́ть в футбо́л ‘play football’игра́ть в пря́тки ‘play hide-and-seek’

2) до того is "until that time" or "until that point" or something like that I think?

You’re right.

Originally Posted by lenssideways8

3) I know как has a lot of different uses. Here I'm not sure what it is. Is it "as Andre came in"?

Yes. Как пришёл Андрей here means something like ‘the event of Andrey’s coming’.
In English one can say e.g. ‘I saw you leaving the house’.
In Russian you cannot use a participle here (technically, you can, but it wouldn’t sound natural). Instead, you can say «Я ви́дел, как ты вы́шел из до́ма», literally, ‘I saw as you left the house’.

Originally Posted by lenssideways8

When we arrived in class, the teacher had already gone home. We had plenty of time to play a game of chess before Andre arrived.